RhoDARTS: Differentiable Quantum Architecture Search with Density Matrix Simulations

Abstract: Variational Quantum Algorithms (VQAs) are a promising approach for leveraging powerful Noisy Intermediate-Scale Quantum (NISQ) computers. When applied to machine learning tasks, VQAs give rise to NISQ-compatible Quantum Neural Networks (QNNs), which have been shown to outperform classical neural networks with a similar number of trainable parameters. While the quantum circuit structures of VQAs for physics simulations are determined by the physical properties of the systems, identifying effective QNN architectures for general machine learning tasks is a difficult challenge due to the lack of domain-specific priors. Indeed, existing Quantum Architecture Search (QAS) algorithms, adaptations of classical neural architecture search techniques, often overlook the inherent quantum nature of the circuits they produce. By approaching QAS from the ground-up and from a quantum perspective, we resolve this limitation by proposing $\rho$DARTS, a differentiable QAS algorithm that models the search process as the evolution of a quantum mixed state, emerging from the search space of quantum architectures. We validate our method by finding circuits for state initialization, Hamiltonian optimization, and image classification. Further, we demonstrate better convergence against existing QAS techniques and show improved robustness levels to noise.